State Republicans say they’ve caught New York’s largest teachers union in a bunch of election-law violations aimed at boosting Democrats, and they’re demanding an investigation.

The charge is certainly credible: When it comes to state Democrats and unions like New York State United Teachers, it’s hard to tell who’s the senior partner.

State GOP Chairman Ed Cox filed a formal complaint with the Board of Elections, charging that NYSUT illegally coordinates its independent expenditure committee and its political action committee.

On the face of it, he’s got an open-and-shut case: There’s supposed to be a firewall between the two, under state law. But both committees share office space and two key officials with NYSUT itself.

As Cox’s complaint points out, you can’t serve both entities without actively coordinating: Regardless of what hats those individuals wear at any particular moment, “you can’t firewall the mind.”

NYSUT, for its part, insists it follows both “the spirit and the letter of the law.” Right.

Then again, this is perhaps the most arrogant special interest in a state full of them. And it has good reason to feel cocky.

Democrats in the Legislature have been its lapdogs since time immemorial. And now, thanks to Assembly Speaker Carl Heastie, NYSUT and its allies (above all, the city United Federation of Teachers) effectively control both the Board of Regents and the state Education Department.

All this power is devoted to just a few goals: 1) expanding and protecting perks and pay for teacher-union members, no matter what the cost to taxpayers, and 2) strangling any and all meaningful public-school reforms — in the cradle, if possible.

Now NYSUT’s been caught thumbing its nose at state election law — presumably convinced its pet politicians will let it get away with (at most) a token fine. Let’s see if any of New York’s countless “clean campaign finance” purists even dare to raise a stink.